What identifier of operator must be entered for assign shortcuts
Please make different topics for each question

For border select you will have to create several entries for selection and deselection with tweak mouse with all the desired modifier keys, like Alt+Tweak+Left or Shit+Tweak+Left, ect. for example.

After that you have to additionally expand the Border select modal key map bellow any of the entries (they are all the same) and manually configure all options for selection, deselection, and canceling the operator. 



I use a similar setup myself, and it is a sort of a chore and a bit hit and miss manual work.

Word of advice, don't directly use Left Mouse or Right Mouse in your keymaps, when possible use Select Mouse or Deselect Mouse so the custom keymap remains dynamic and responds to general switch of selection with left or right click. Also make sure there are no conflicts as they may inexplicably make some key assignments nor work

Best way to know an operator name is to Right Click a button and choose one of the following options and search for hints there


Copy Python Command
Copy Data Path
Online Python Reference
Assign Shortcut (does it automatically)
Edit Source


Some times it's also useful to search for that operator in the keymap list and see if there's one already assigned you can copy from.
Some buttons don't use an operator directly though, some times they need contexts, or toggle variables or call menus.

For toggling occluded geometry the operator has to be wm.context_toggle and the context is space_data.use_occlude_geometry